Fun with figures by KENNETH WILLIAMS

When BharatiKrsna Tirthaji reconstructed the ancient system ofVedic Maths used in this book earlier this century, heuncovered a beautifully integrated and complete sys-tem of maths which

FUN WITH F GURES

BRILLIANT MENTAL MATHS

SHORT CUTS THAT WILL AMAZE EVERYONE!

KENNETH WILLIAMS

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On seeing this kind of work actually beingperformed by the little children, the doc-tors, professors and other “big guns” of mathe-matics are wonder-struck and exclaim:

‘Is this mathematics or magic?’

And we invariably answer and say: ‘It is both

It is magic until you understand it;

and it is mathematics thereafter’

Bharati Krsna Tirthaji

Vedic Mathematics Scholar

Ten-year old Truman Henry Safford (born 1836) wasasked:

“Multiply in your head

365,365,365,365,365,365

by

365,365,365,365,365,365.”

He flew around the room like

a top, pulled his pantaloons

over the top of his boots,

bit his hand, rolled his

eyes in their sockets,

sometimes smiling and

talking, and then seeming to

be in an agony, until, in not more

than one minute, said he,

“133,491,850,208,566,925,016,658,299,941,583,225!”

‘Lightning calculators’, are not that uncommon andwhile we may not be able to match the brilliance of aTruman Henry Safford, we can all develop, with theaid of this book, a talent at mental mathematics With these super-easy methods you need no longer be

I N T R O D U C T I O N

caught between the drudgery of the old dinosaur ods and the ‘cop-out’ of the calculator When BharatiKrsna Tirthaji reconstructed the ancient system ofVedic Maths (used in this book) earlier this century, heuncovered a beautifully integrated and complete sys-tem of maths which had been lost for centuries TheVedic system mirrors the way the mind naturally worksand so is designed to be done mentally.

meth-Fun with Figures is for those who think they are no

good at maths – and for those who are good atmaths It is for those who would like to steal a littlelightning The book answers a need of our time,offering easy, enjoyable maths which improves men-tal agility and memory, promotes confidence and cre-ativity – as well as being useful in everyday life.Each double page shows a simple mathematicalmethod and is independent of the others (with twoexceptions, which are indicated) In addition to thevarious everyday situations indicated in this book,you will surely find many other occasions for the use

of these easy methods There are many exercises foryou to practise and answers at the end of the book

16 EXERCISE YOUR BRAIN CELLS

18 SHOW YOUR CLASS

20 ON A WALK

22 AT THE OFFICE

24 ON THE MOTORWAY

26 THE NINE-POINT CIRCLE

28 IN YOUR MATHS LESSON

30 CHECK YOUR BILL

34 IN THE DIY SHOP

36 HAVE A BREAK

38 AT THE POST OFFICE

40 IMPRESS YOUR PARENTS

42 DELIGHT YOUR CHILD

44 IMPROVE YOUR MIND

46 ON THE TRAIN

52 RELATED BOOKS

A M A Z E Y O U R F R I E N D S

8

Use the formula ALL FROM 9 AND THE LAST FROM 10 to amaze your friends with instant sub- tractions.

And that’s all there is to it!

This always works for subtractions from numbersconsisting of a 1 followed by noughts: 100; 1000;10,000 etc

So 1000 - 83 becomes 1000 - 083 = 917

Try some yourself:

1) 1000 - 777 = 2) 1000 - 283 = 3) 1000 - 505 = 4) 10,000 - 2345 = 5) 10000 - 9876 = 6) 10,000 - 1101 = 7) 100 - 57 = 8) 1000 - 57 =

9) 10,000 - 321 = 10)10,000 - 38 =

Mathematics, rightly viewed, possesses not only truth but supreme beauty

BERTRAND RUSSELL

I N T H E S H O P

10

Instantly find the change due from $10 or $20

„ Suppose you buy something for $3.33 and yougive a $10 note How much change would youexpect to get?

You just apply ALL FROM 9 AND THE LASTFROM 10 to the $3.33 and you get $6.67:

from 9 from 9 from 10

Zerah Colburn (1804-40), when he was eight, was asked to raise the number 8 to the sixteenth power: he announced the answer

(281,474,976,710,656) “promptly and with ity”, causing the academic audience to weep He was next asked to raise the numbers 2,3, 9 to the 10th power: and he gave the answers so rap- idly that the gentleman who was taking them down was obliged to ask him to repeat them more slowly.

facil-11

„ $10 - $2.30 = $7.70

Here “the last” is the 3 as zero does not count

So we take 2 from 9 and 3 from 10

Try these:

1) $10 - $7.77 = 2) $10 - $4.44 = 3) $10 - $6.36 = 4) $10 - $5.67 = 5) $100 - $84.24 = 6) $100 - $31.33 =

TA B L E S M A G I C

12

Don’t know your tables? Never mind, in this system you don’t need them beyond 5 x 5!

„ Suppose you need 8 x 7

8 is 2 below 10 and 7 is 3 below 10

Think of it like this:

The whole heaven is number and harmony

ARISTOTLE

13

You subtract crosswise: 8 - 3 or 7 - 2 to get 5,

the first figure of the answer

And you multiply vertically: 2 x 3 to get 6,

the last figure of the answer

That’s all you do:

see how far the numbers are below 10, subtract onenumber’s deficiency from the other number, andmultiply the deficiencies together

AT A PA R T Y

14

At a party surprise your friends with this spectacular way of multiplying large numbers together in your head.

Here’s how to use VERTICALLY AND WISE for multiplying numbers close to 100

CROSS-„ Suppose you want to multiply 88 by 98.

Not easy, you might think But with

VERTICAL-LY AND CROSSWISE you can give the answerimmediately, using the same method as on thelast page

Both 88 and 98 are close to 100

88 is 12 below 100 and 98 is 2 below 100.You can imagine the sum set out like this:

Where there is life there is pattern and where there is pattern there is mathematics

(or 98 - 12 = 86: you can subtract

either way, you will always get

the same answer)

And the 24 in the answer is

just 12 x 2: you multiply vertically

While waiting in a queue,

why not exercise your brain

cells by multiplying numbers

I proposed to him [Jedediah Buxton, 1702-72] the follow- ing random question:

In a body whose 3 sides are 23,145,789 yards, 5,642,732 yards, and 54,965 yards, how many cubical eighths of an inch? After once naming the sever-

al figures distinctly, one after another, in order to assure himself of the several dimensions and fix them in his mind, without more ado he fell to work amidst more than 100 of his fellow labor- ers, and after leaving him about 5 hours, on some necessary concerns (in which time I calcu- lated it with my pen) at my return, he told me he was ready: upon which, taking out my pocket book and pencil, to note down his answer, he asked which end I would begin at, for he would direct me either way I chose the regular method and in a line of 28 figures, he made

no hesitation nor the least mistake.

nature is the isation of the simplest conceivable mathe- matical ideas.

Out walking with your friends, show them this quick way to square numbers that end in 5 using the for- mula BY ONE MORE THAN THE ONE BEFORE.

„ 75 2 = 5625

752 means 75 x 75

The answer is in two parts: 56 and 25

The last part is always 25.

20

O N A WA L K

For the harmony

of the world is made manifest in Form and Number, and the heart and soul and all the poetry

of Natural Philosophy are embodied in the concept of mathematical beauty.

Show your colleagues in the office this beautiful method for multiplying numbers where the first figures are the same and the last figures add up to 10.

„ 32 x 38 = 1216

Both numbers here start with 3 and the last ures (2 and 8) add up to 10

fig-So we just multiply 3 by 4 (the next number up)

to get 12 for the first part of the answer.

And we multiply the last figures: 2 x 8 = 16 toget the last part of the answer

22

AT T H E O F F I C E

The mathematician does not study pure mathematics because

it is useful; he ies it because he delights in it and he delights in it because

On a car journey, get the children to find the digit sum of car number plates.

Any number of any size can always be reduced to asingle figure by adding its digits

„ For example 42 has two digits which add up to 6

We say “the digit sum of 42 is 6”

„ The digit sum of 413 is 8 because 4 + 1 + 3 = 8

„ For 20511 the digit sum is 9

Try a few:

1) 34 2) 61 3) 303 4) 3041 5) 21212

24

O N T H E M O T O R WAY

All things that can

be known have ber; for it is not pos- sible that without numbers anything can be either con- ceived or known.